1. Field of the Invention
The present invention relates to a testing system, a computer implemented testing method, and a method for manufacturing electronic devices, which are suitable for manufacturing a semiconductor device.
2. Description of the Related Art
There are a variety of processes such as deposition, lithography and etching in a manufacturing process of a semiconductor device. After completion of each process, a test to determine whether or not the semiconductor device has been desirably processed is performed. As examples of such tests, there are: a film-thickness measurement, which is performed after the deposition process, such as CVD and sputtering, an overlay error test, which is performed after the lithography, a critical dimensional measurement, which is performed after the lithography and the etching.
Needless to say, data accuracy is required in such tests. Specifically, it is most important to obtain mean values, variations and the like of film thickness, dimensions and the like. However, complete test of all chip areas in a manufacturing process is actually impossible, and usually, a sample testing is performed by properly sampling only some chip areas or wafers. For example, In normal lithography, a lot composed of approximately 25 wafers is defined as one processing unit. In an overlay error test of such lots, at most approximately five wafers are sampled from each lot, approximately 10 chip areas per wafer are selected, of which overlay errors are then measured, and values obtained by the measurement are taken as a mean value of the lot. The mean value obtained by such a sample testing is a “sample mean” referred to in statistics, and is an estimate of a mean (population mean) of the whole of the lot (population).
Now, it is assumed that the overlay errors in the lot follow a normal distribution N(μ, σ2) (where μ is the population mean, and σ is a known standard deviation). When an idea of the interval estimation is used in a case of estimating the population mean μ from a sample mean x obtained from n samples, a range where the population mean μ exists in a probability of 95% (95% confidence interval) is represented by the following Equation (1):x−1.96σ/(n)1/2<μ<x+1.96σ/(n)1/2  (1)
However, in the case of using Equation (1), the range of the confidence interval changes depending on the standard deviation σ and the number n of samples in the lot, and accordingly, estimation accuracy for the population mean μ varies. Particularly, when the standard deviation σ is large and the number n of samples is small, the estimation accuracy for the population mean μ lowers, thus adversely affecting the full comprehension and control of process capabilities. Meanwhile, in the case of performing the test for the constant number n of samples, the confidence interval of data becomes varied depending on the standard deviation σ of each lot. Therefore, the obtainment of the confidence interval by use of Equation (1) is disadvantageous for highly accurate process control.